A CSI Approach Incorporating Recursive Eigenfunction Expansion for Efficient Microwave Imaging of Objects Embedded in Arbitrarily Shaped Multilayer Cylinders

Microwave imaging of objects embedded in multilayer cylindrical structures is of practical importance in applications where inaccessible targets are surrounded by a known inhomogeneous host. In such problems, incorporating the known multilayer structure into the background model can improve reconstruction accuracy and reduce the complexity of the inverse problem. This paper presents an efficient imaging method for dielectric objects embedded in two-dimensional multilayer cylindrical structures with arbitrarily shaped layer boundaries. The proposed approach integrates the contrast source inversion method with a recursive eigenfunction expansion technique for noncircular geometries. The known multilayer host is treated as the background medium, while the inversion is restricted to the embedded scatterers. The recursive formulation is derived to compute the inhomogeneous-background Green’s function and the required cell-integrated Green’s functions in a semi-analytical and discretization-free manner. Numerical results suggest that the method is capable of providing satisfactory reconstructions of embedded objects under various host configurations, including cases with a Perfect Electric Conductor (PEC) core. Comparisons with Method of Moments reference solutions confirm the accuracy of the forward modeling and the reliability of the inversion, while demonstrating a significant reduction in computational cost.